Miller Indices Calculator

Miller Indices Calculator

Convert axis intercepts into the smallest integer Miller index triplet.

Last updated: June 2026 | By Patchworkr Team

Intercepts
Miller Indices
(1 1 1)
Reciprocals: 1/1, 1/1, 1/1

What are Miller Indices?

Miller indices are the smallest integer triplet proportional to the reciprocals of the intercepts.

1. Take reciprocals of the intercepts.
2. Clear denominators to get integers.
3. Reduce by the greatest common divisor.

A zero intercept reciprocal becomes 0 because the plane is parallel to that axis.

How to Use

1. Enter the a, b, and c intercepts in lattice units.

2. Use inf for a plane parallel to an axis.

3. Read the live integer Miller indices.

Worked Example

For intercepts 2, 3, and 1:

reciprocals = 1/2, 1/3, 1

clearing denominators gives (3, 2, 6)

The calculator should show (3 2 6).

FAQ

Can I enter decimals?

Yes. The tool converts finite decimals into rational fractions first.

What does inf mean?

The plane is parallel to that axis, so the reciprocal is 0.

Can indices be negative?

Yes. Negative intercepts produce negative Miller indices.

Why are the indices integers?

Because the reciprocal ratios are scaled to the smallest whole-number triplet.

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